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United States Defense Secretary Ashton Carter promised yesterday to resolve the cases of thousands of Army National Guard soldiers who were ordered by the Defense Department to repay bonuses they received to enlist in the military.

"We are going to look into and resolve it," he said, adding that Deputy Defense Secretary Robert Work is examining the situation. "It is a significant issue."

An estimated 10,000 soldiers with the California Army National Guard were told they had to pay back enlistment bonuses of at least US$10,000 to US$15,000 each because they were improperly issued during the height of the Pentagon's wars in Iraq and Afghanistan, and the issue likely extends to other states, defense officials acknowledged earlier this week. The California cases, first reported on Saturday by the Los Angeles Times, are tied to a criminal investigation in which soldiers unknowingly accepted bonuses from recruiters that were not authorised.

The issue has prompted outcry on Capitol Hill, although Major General Matthew Beevers, the No. 2 officer in the California Army National Guard, said that Guard leaders attempted to resolve the problem through Congress two years ago, and the effort stalled. Beevers said that an effort to pass legislation that would have provided relief to affected soldiers was met negatively by the Congressional Budget Office because it would have added spending at a time when the US government was attempting to cut back.

"It's important to note that we've kind of led the way in trying to solve this," the general said.

The California cases prompted a broad audit by the California Army National Guard that concluded recently. It found that about $30 million was not properly authorised, but also showed that 4000 soldiers, who also could have been ordered to pay back a combined US$37.2 million, received them according to existing policies. Those soldiers were allowed to keep their money, Beevers said.

One soldier involved in issuing the bonuses, Master Sgt. Toni Jaffe, pleaded guilty in 2011 to filing false claims while serving as incentive manager for the California Army National Guard. Beevers said that at least three other senior members of the Guard lost their jobs, and others faced administrative punishments.

A bipartisan group of lawmakers have called for additional oversight and quick action by the Defense Department. In one letter issued Monday, Senators Dianne Feinstein and Barbara Boxer said the actions taken thus far have been "unfair and appalling" and called for Carter to intervene directly.

"Thousands of our service members are paying the price for mistakes made by California National Guard managers, some of whom are now serving jail time or paying restitution for their crimes," the letter said. "It is outrageous to hold these service members and their families responsible for the illegal behaviour of others."

The House Committee on Oversight and Government Reform launched an investigation Monday and requested all documents associated with the California cases in a letter to General Joseph Lengyel, the senior officer for the National Guard Bureau, and Maj. Gen. David Baldwin, the top officer in the California National Guard. They also asked for the officers to brief committee members by November 17.

"The Committee is seeking information about this serious matter, and to see that officials who mismanaged bonus programs are held accountable," said the letter.